Abstract

We have theoretically studied the effect of deterministic temporal control of spontaneous emission in a dynamic optical microcavity. We propose a new paradigm in light emission: we envision an ensemble of two-level emitters in an environment where the local density of optical states is modified on a time scale shorter than the decay time. A rate equation model is developed for the excited state population of two-level emitters in a time-dependent environment in the weak coupling regime in quantum electrodynamics. As a realistic experimental system, we consider emitters in a semiconductor microcavity that is switched by free-carrier excitation. We demonstrate that a short temporal increase of the radiative decay rate depletes the excited state and drastically increases the emission intensity during the switch time. The resulting time-dependent spontaneous emission shows a distribution of photon arrival times that strongly deviates from the usual exponential decay: A deterministic burst of photons is spontaneously emitted during the switch event.

The resonant index change contribution from the excited emitters themselves can be neglected due to the low emitter density. Likewise the emission frequency shift caused by the refractive index change of the of the surrendering material is small compared to the cavity resonance shift and has been neglected.

Ultrashort Processes in Condensed Matter (1)

Other (5)

The resonant index change contribution from the excited emitters themselves can be neglected due to the low emitter density. Likewise the emission frequency shift caused by the refractive index change of the of the surrendering material is small compared to the cavity resonance shift and has been neglected.

Figures (4)

Schematic graph of the switching process as experienced by a quantum emitter (green) emitting at a frequency ωd in the spectral vicinity of a cavity resonance whose frequency is switched in time. The cavity has a Lorentzian local density of states (solid line). Initially the emitter is detuned from the cavity resonance ωcav,0by nearly one cavity linewidth, leading to an effective radiative rate Γ0. The switching process moves the cavity resonance up in frequency ωcav(t) (gray dashed). The cavity is then tuned into resonance with the emitter that thus experiences a decay rate strongly enhanced by ΔΓrad. Within one cavity linewidth from the resonance, switching of the cavity resonance can be approximated by a linear shift of the decay rate versus frequency (red dashed line).

Radiative decay rate normalized to the unswitched rate Γ0(solid line) as a function of time after exciting the emitter. The two thick curves show the result of a switching event at t0pu = 10 ps that either enhances (long dashed) or inhibits (short dashed) the decay rate by a factor of 5. The modified decay rate relaxes back to the unswitched rate within the effective switching time of τsw = 35 ps after the switching event.

(a) Time resolved population density for an emitter excited at t = texc = 0 ps showing the effect of two different switch events at t = tpu = 150 ps. The chosen parameters model the effect of a switch event that either tunes a cavity resonance into (green long dashed) or out of (red short dashed) resonance with the emitter frequency. Without switch the populations decay exponentially with a rate of Γ0 = 1 ns−1and Γ0 = 5 ns−1, respectively, in the two examples (solid lines). The switch event leads to an enhanced or inhibited radiative rate by a factor of 5 relative to the unswitched rate. These time-dependent rates result in a short decrease or increase in the populations relative to the unswitched cases. At long times after the effective switching time τsw = 35 ps, the slopes tend to their initial values for both examples. (b) The corresponding spontaneous emission intensities from the emitter relative to the initial values after excitation for the same two examples presented in (a). The small changes in the population density corresponds to large changes in the emitted intensity. Switching the cavity into resonance with the quantum dot (green long dashed) results in a sharp burst of intensity with a temporal duration of τsw. Tuning out of resonance leads to a fast drop in the intensity.

The effect of free carrier absorption on the time resolved emitted intensity for emitters embedded in a switched cavity. After the emitter is excited at t = tex = 0 ps the cavity resonance is switched one linewidth S = Δω/γi = 1 at t = tpu = 150 ps. At this time the radiative decay rate is increased by ΔΓrad = 4Γ0from Γ0 = 1 ns−1. Afterwards the resonance frequency relaxes exponentially back to its original value with a switching time ofτsw = 35 ps. The black dashed line shows the emitted intensity neglecting the effect of free carrier absorption whereas the red line include absorption with a = 0.083 extracted from [47]. The free carrier absorption only inflict a reduction of 15% on the height of the peak intensity.